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# a,b,c, and d are the position vectors of four coplanar points such that (a-d).(b-c)=(b-d).(c-a)=0  .  Show that the point d represents the orthocentre of the triangle with a,b and c as its vertices

Arun
25763 Points
3 years ago
Dear student

First equation means that
AD$\perp$ BC
Second equation means
BD $\perp$ CA
Then D is the intersection of altitudes through A and B. Hence D is orthocentre.